Question

The image above shows a wire formed from two circular shapes: The larger circle has a radius of 6cm, and the smaller circle has a radius of 3cm. Each of the 8 circular arcs subtends an angle of 45° A current of 50 A flows in the wire. What is the magnitude of the magnetic field at the center of this object? Text description of the image: The shape shown is built from alternating 45° circular arcs of each circle connected by radiallines: You can build the shape by using two concentric circles: Go clockwise 45° along an arc of the smaller circle, go out radially to the larger circle, go clockwise 45° along an arc of the larger circle, go in radially to the smaller circle, and repeat the process until you return to the starting point. The final shape resembles a cross.

Answer 1

I-50A Inner circle has radius - 3cm 459 450 Alison 3om Outer radius -bum 45° ram 45° Current in wire - 50 A 1 Magnetic field Now, field at centre o due to inner circular wires in B,= 4. Mo I. 7/4 MoI 408, 48, urx107x50 H 4 x 3 x 10-2 = 52.36x 105 H And magnetic field at centre o due to outer circular wires is Molly B₂ = 4. Mol 4082 482

thus, B₂ = 4 x 10-7 * 50 4x 6x102 B₂ = 26.18x10-5H magnetic are in Since both field at the centre o same direction i.e. lackwise ® thus et magnitude of magnetic field at centre is B = BitB₂ = 52.36x10-5+ 26-18x10.5 B=78.54 x 105 H X